What is the d/(dt)(t^2+(2t)/(sqrt(t))-1/(t^2)) ?

The d/(dt)(t^2+(2t)/(sqrt(t))-1/(t^2)) is (t^{5/2}+2+2t^4)/(t^{5/2)sqrt(t)}

What is the first d/(dt)(t^2+(2t)/(sqrt(t))-1/(t^2)) ?

The first d/(dt)(t^2+(2t)/(sqrt(t))-1/(t^2)) is (t^{5/2}+2+2t^4)/(t^{5/2)sqrt(t)}

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\frac{d}{d t} (t^{2} + \frac{2 t}{t} - \frac{1}{t ^{2}})

\frac{t ^{\frac{5}{2}} + 2 + 2 t ^{4}}{t ^{\frac{5}{2}} t}

Solution steps

\frac{d}{d t} (t^{2} + \frac{2 t}{t} - \frac{1}{t ^{2}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d t} (t^{2}) + \frac{d}{d t} (\frac{2 t}{t}) - \frac{d}{d t} (\frac{1}{t ^{2}})

\frac{d}{d t} (t^{2}) = 2 t

\frac{d}{d t} (\frac{2 t}{t}) = \frac{1}{t}

\frac{d}{d t} (\frac{1}{t ^{2}}) = - \frac{2}{t ^{3}}

= 2 t + \frac{1}{t} - (- \frac{2}{t ^{3}})

Simplify

2 t + \frac{1}{t} - (- \frac{2}{t ^{3}}) : \frac{t ^{\frac{5}{2}} + 2 + 2 t ^{4}}{t ^{\frac{5}{2}} t}

= \frac{t ^{\frac{5}{2}} + 2 + 2 t ^{4}}{t ^{\frac{5}{2}} t}

What is the d/(dt)(t^2+(2t)/(sqrt(t))-1/(t^2)) ?
The d/(dt)(t^2+(2t)/(sqrt(t))-1/(t^2)) is (t^{5/2}+2+2t^4)/(t^{5/2)sqrt(t)}
What is the first d/(dt)(t^2+(2t)/(sqrt(t))-1/(t^2)) ?
The first d/(dt)(t^2+(2t)/(sqrt(t))-1/(t^2)) is (t^{5/2}+2+2t^4)/(t^{5/2)sqrt(t)}